The Probability of Coin Flips
A fair coin has exactly 50% chance of landing on heads and 50% chance of landing on tails. However, in small sample sizes, you may see significant deviation from this expected ratio. This is called variance.
The more flips you perform, the closer your results will get to the theoretical 50/50 split. This principle is known as the Law of Large Numbers - a fundamental concept in probability theory and statistics.
Features
- Realistic Animation: Smooth 3D coin flip animation
- Live Statistics: Track heads, tails, and percentages in real-time
- Multiple Flips: Flip up to 100 coins at once
- Streak Tracking: See your current winning streak
- Persistent Stats: Statistics saved automatically
- Sound Effects: Optional coin flip sound (Web Audio API)
Use Cases
Decision Making
Can't decide between two options? Let the coin decide! A coin flip is the ultimate unbiased decision maker for 50/50 choices.
Sports & Games
Determine who goes first in games, sports matches, or competitions. Perfect for kickoffs, serve decisions, or turn order.
Teaching Probability
Demonstrate probability concepts to students. Show how random events converge to theoretical probabilities over many trials.
Random Selection
Fairly choose between two people, teams, or options. The coin flip has been trusted for centuries as a fair selection method.
Understanding Coin Flip Probability
While each individual flip has a 50% chance of being heads or tails, interesting patterns emerge over multiple flips:
- Gamblers Fallacy: Past results don't affect future flips - each flip is independent
- Streaks are Normal: Long streaks of heads or tails are mathematically expected in large samples
- Regression to Mean: Extreme results tend to balance out over time
- Sample Size Matters: Small samples can show wild variation; large samples stabilize
Fun Coin Flip Facts
- The longest recorded streak of heads in 100 flips was 13 consecutive heads
- A coin flipped 10,000 times will typically land within 49.5% to 50.5% heads
- Physical coins have a slight bias based on which side starts facing up
- The NFL has used a coin toss for the opening kickoff since 1892